Finite Group Databasebeta

← C2×D3×D20 #92012

Subgroups — C2×D3×D20 #92012

Order 480.

472 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D5C212yesmaximal, complemented
2C2×D60C211yesmaximal, characteristic, complemented
3C2×C4×C5×D3C211yesmaximal, characteristic, complemented
4C2×C3×D20C211yesmaximal, characteristic, complemented
5C2×#1202C212yesmaximal, complemented
6D3×D20C218yesmaximal, direct product factor
7C22×D20—31nomaximal, Hall
8C22×D15C2212yescomplemented
9C22×C5×D3C2211yescharacteristic
10C22×C3×D5C2212yescomplemented
11C2×D3×D5—28no—
12C2×D3×D5C2218yescomplemented
13C2×C3×C4×C5C2211yescharacteristic, complemented
14D60C2214yescomplemented
15C2×C5×Dic3C2211yescharacteristic, complemented
16C4×C5×D3C2214yescomplemented
17C3×D20C2214yescomplemented
18#1202C2218yescomplemented
19C2×D3×D4—51nomaximal, Hall
20C23×D5—32no—
21C22×C4×C5—31no—
22C2×D20—32no—
23C2×D20—31no—
24C2×D20—38no—
25C2×D20D311yescharacteristic, direct product factor
26C22×C3×C5C2311yescharacteristic
27C2×D15—24no—
28C2×D15C2314yescomplemented
29C2×C5×D3D414yescomplemented
30C2×C5×D3C2312yes—
31C2×C3×D5—24no—
32C2×C3×D5C2314yescomplemented
33D3×D5—216no—
34C3×C4×C5C2312yescomplemented
35C5×Dic3C2312yescomplemented
36C23×D3—52no—
37C2×C3×D4—51no—
38C2×#67—52no—
39D3×D4—58no—
40C2×D12—51no—
41C2×C4×D3D511yescharacteristic, complemented
42C23×C5—31no—
43C22×D5—32no—
44C22×D5—38no—
45C22×D5—68no—
46C22×D5C2×D312yescomplemented
47C2×C4×C5—31no—
48C2×C4×C5—34no—
49C2×C4×C5C2×D311yescharacteristic, complemented
50D20—38no—
51D20—34no—
52D20C2×D314yesdirect product factor
53C22×D4—151noSylow
54C2×C3×C5C2×D412yescomplemented
55C2×C3×C5C2411yescharacteristic
56D15—24no—
57C3×D5—24no—
58C5×D3C2×D414yescomplemented
59C23×C3—52no—
60C22×D3—52no—
61C22×D3—58no—
62C22×D3—108no—
63C22×D3C2×D511yescharacteristic
64C3×D4—54no—
65C2×C3×C4C2×D511yescharacteristic, complemented
66#67—58no—
67C2×Dic3C2×D511yescharacteristic, complemented
68D12—54no—
69C4×D3C2×D514yescomplemented
70C22×C5—34no—
71C22×C5—32no—
72C22×C5C22×D311yescharacteristic
73C2×D5—24no—
74C2×D5—34no—
75C2×D5—616no—
76C2×D5—64no—
77C2×D5C22×D314yescomplemented
78C4×C5—32no—
79C4×C5C22×D312yescomplemented
80C24—152no—
81C2×D4—51no—
82C2×D4—158no—
83C2×D4—152no—
84C2×D4—151no—
85C22×C4—31no—
86C3×C5C22×D411yescharacteristic, complemented, Hall
87C22×C3—54no—
88C22×C3—104no—
89C22×C3C22×D511yescharacteristic
90C2×D3—54no—
91C2×D3—104no—
92C2×D3—1016no—
93C2×D3D2014yesdirect product factor
94C2×D3C22×D512yes—
95C3×C4C22×D512yescomplemented
96Dic3C22×D512yescomplemented
97C2×C5—34no—
98C2×C5D3×D412yescomplemented
99C2×C5C23×D311yescharacteristic
100D5—24no—
101D5—64no—
102C23—31no—
103C23—52no—
104C23—158no—
105C23—152no—
106C23—308no—
107D4—54no—
108D4—158no—
109D4—154no—
110C2×C4—31no—
111C2×C4—34no—
112C2×C4D3×D511yescharacteristic, complemented
113C2×C3—104no—
114C2×C3C2×D2012yescomplemented
115C2×C3C23×D511yescharacteristic
116D3—104no—
117D3C2×D2014yesdirect product factor
118C5C2×D3×D411yescharacteristic, complemented, Sylow
119C22—34no—
120C22—32no—
121C22—54no—
122C22—104no—
123C22—154no—
124C22—3016no—
125C22—304no—
126C22C2×D3×D511yescharacteristic
127C4—32no—
128C4C2×D3×D512yescomplemented
129C3C22×D2011yescharacteristic, complemented, Sylow
130C2—34no—
131C2—104no—
132C2—304no—
133C2D3×D2012yesdirect product factor
134C2C22×D3×D511yescharacteristic
subgroupG/H
centerC22C2×D3×D5
commutator, cosocleC2×C3×C5C24
FrattiniC2C22×D3×D5
FittingC2×C3×C4×C5C22
socleC22×C3×C5C23
hypercenterC2×C4D3×D5
hypocenterC3×C5C22×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×D3×D5C2semidirect
2. C2×D60C2semidirect
3. C2×C4×C5×D3C2semidirect
4. C2×C3×D20C2semidirect
5. C2×#1202C2semidirect
6. D3×D20C2direct (N × H)
8. C22×D15C22semidirect
10. C22×C3×D5C22semidirect
12. C2×D3×D5C22semidirect
13. C2×C3×C4×C5C22semidirect
14. D60C22semidirect
15. C2×C5×Dic3C22semidirect
16. C4×C5×D3C22semidirect
17. C3×D20C22semidirect
18. #1202C22semidirect
25. C2×D20D3direct (N × H)
28. C2×D15C23semidirect
29. C2×C5×D3D4semidirect
32. C2×C3×D5C23semidirect
34. C3×C4×C5C23semidirect
35. C5×Dic3C23semidirect
41. C2×C4×D3D5semidirect
46. C22×D5C2×D3semidirect
49. C2×C4×C5C2×D3semidirect
52. D20C2×D3direct (N × H)
54. C2×C3×C5C2×D4semidirect
58. C5×D3C2×D4semidirect
65. C2×C3×C4C2×D5semidirect
67. C2×Dic3C2×D5semidirect
69. C4×D3C2×D5semidirect
77. C2×D5C22×D3semidirect
79. C4×C5C22×D3semidirect
86. C3×C5C22×D4semidirect
93. C2×D3D20direct (N × H)
95. C3×C4C22×D5semidirect
96. Dic3C22×D5semidirect
98. C2×C5D3×D4semidirect
112. C2×C4D3×D5semidirect
114. C2×C3C2×D20semidirect
117. D3C2×D20direct (N × H)
118. C5C2×D3×D4semidirect
128. C4C2×D3×D5semidirect
129. C3C22×D20semidirect
133. C2D3×D20direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D3×D52
C2×D602
C2×C4×C5×D32
C2×C3×D202
C2×#12022
D3×D202
C22×D203
C2×D3×D45